Visualising Solid Shapes

Plane figures or shapes have two measurements namely length and breadth. Hence, they are called two-dimensional shapes whereas a solid object has three measurements namely length, breadth, height or depth. Hence, they are called three-dimensional shapes. Also, a solid shape occupies some space. Two-dimensional and three-dimensional figures can also be briefly named as 2-D and 3-D figures, respectively. Some two-dimensional figures are shown below.

Two-dimensional figures

Some three-dimensional figures are shown below:

Three-dimensional figures

Three-dimensional figures have different numbers of faces, edges and vertices. All the flat surfaces of the figure are called faces, these faces are 2-D shapes. The line segment where the faces of three-dimensional figures meet each other is called the edge of the shape. The corners or points where the edges of the figure meet each other are called vertices (if one such point is there, then it is called a vertex).

Read more:

Three Dimensional Geometry

2d shapes

3d shapes

Important Questions Class 8 Maths Chapter 10 Visualising Solid Shapes

Consider a cuboid, the faces, edges and vertices are shown below:

Cuboid and Edges

The number of faces = 6

Number of edges = 12

Number of vertices = 8

Three-dimensional shapes are further classified into two types.

  1. Polyhedrons (or regular polyhedrons)
  2. Three-dimensional figures with curved surfaces

Polyhedrons, Prism and Pyramid

Name Shape Properties
Cube Faces = 6

Edges = 12

Vertices =8

Cuboid Cuboid 2 Faces = 6

Edges = 12

Vertices =8

Prism (Triangular prism) Triangular prism Faces = 5

Edges = 9

Vertices = 6

Pyramid (square based pyramid) Square based pyramid Faces = 5

Edges = 8

Vertices = 5

Triangular pyramid Triangular pyramid Faces = 4

Edges = 6

Vertices = 4

Three-dimensional figures with curved faces

Name Shape Properties
Cylinder Cylinder 1 Faces = 3

(curved faces = 1, places surfaces =2)

Edges = 2

Vertices = 0

Cone Cone 1 Faces = 2

(curved face = 1, plane surface = 1)

Edges = 2

Vertices = 1

Sphere Sphere 1 Faces = 1 (curved surface)

Edges = 0

Vertices = 0

Nets for building 3-D shapes

A two-dimensional shape that can be folded to form a three-dimensional shape or a solid is referred to as a geometry net. When the surface of a three-dimensional shape is laid out flat showing each face of the shape, the obtained pattern is called a net. A solid may have different nets. In simple words, net is an unfolded form of a 3D figure.

Shape Solid Net
Cube Cube 2 Net of cube
Cuboid Cuboid 2 Net of cuboid
Triangular prism Triangular prism 2 Net of triangular prism
Square pyramid Square based pyramid 2 Net of square pyramid
Triangular pyramid Triangular pyramid 2 Net of triangular pyramid
Cylinder Cylinder 2 Net of cylinder
Cone Cone 2 Net of cone

Different views of a solid shape

A three-dimensional object or shape can look differently from different positions (or sides) so they can be drawn from different perspectives, this is called visualising a solid shape. For example, views of a hut and a solid with three cubes from different sides are given below.

Example 1:

Views of a solid shape 1

As shown in the above, front view of a hut is the combination of a square with a conical top, side view and top view is the combination of two rectangular surfaces.

Example 2:

Views of a solid shape 2

In the above figure, one side of a solid has two square surfaces which are vertically connected, front view gas three square surfaces in L shape and top view has two square surfaces which are horizontally connected.

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